Yes, there is. Take the metro (subway). You can get a combination train/subway ticket in Civ and you would pay a LOT less than a taxi is going to cost you. The metro station is right there at the Termini station where you will be arriving from Civ. There is a Metro station about 1/4 to 1/2 mile from the Vatican. Taking a Taxi from the termini station is an option but with traffic, I'm not sure its a time saver.